Negative Refractive Index Device for Generating Terahertz or Microwave Radiation and Method of Operation Thereof

ABSTRACT

A negative refractive index device and a method of generating radiation. In one embodiment, the device includes: (1) an optical input configured to receive light and (2) an optical medium having a negative index of refraction and a second-order nonlinearity proximate a center frequency of the light, coupled to the optical input and configured to resonate in response to the light to yield radiation having a phase velocity based on a group velocity of the light.

TECHNICAL FIELD OF THE INVENTION

The invention is directed, in general, to and, more specifically, to anegative refractive index device for generating terahertz or microwaveradiation and a method of generating such radiation.

BACKGROUND OF THE INVENTION

Terahertz radiation, sometimes called “T-rays,” remains a relativelyunexplored region of the electromagnetic spectrum. Terahertz radiationlies in the frequency band between about 10¹¹ Hertz (Hz) and about5×10¹³ Hz and therefore between microwaves and infrared light. Terahertzradiation is important, because it has potential use in many military,security, commercial, biomedical, pharmaceutical and scientific researchapplications. Terahertz radiation can penetrate most solid substance andso behave like X-rays. Unlike X-rays however, terahertz radiation isnon-ionizing and thus substantially safer to use. Terahertz radiationalso can produce images of higher resolution than X-rays. Because ofterahertz radiation's ability to penetrate fabrics and plastics, it canbe used in surveillance, including security screening, to uncoverconcealed weapons on a person. This is highly useful, because manymaterials of interest, such as plastic explosives, exhibit uniquespectral “fingerprints” in the terahertz range. This offers thepossibility of combining spectral identification with imaging. Terahertzradiation can also be used to characterize semiconductors moreaccurately and widen wireless communication frequency bands.

Because they can penetrate several centimeters into human flesh,terahertz radiation can detect tumors far better than today's mammogramsand can detect skin cancer before it appears as lesions on the skin.Coupled with tomography algorithms, terahertz radiation can be used tocreate a 3-D map of the human body that has a far higher resolution thanone produced by nuclear magnetic resonance (NMR), paving the way for ahost of diseases to be detected earlier and more effectively.

A heavy demand for terahertz radiation also exists in the communicationsindustry. For example, a terahertz-frequency heterodyne receiver candramatically increase the available bandwidth inwavelength-division-multiplexed (WDM) communication systems.

However, while the benefits of having terahertz radiation have beenunderstood for over a decade, having a powerful source of terahertzradiation has eluded technologists so far. Currently, two basictechniques for generating terahertz radiation are used: photoconductionand nonlinear optical frequency conversion. Electrically biasedhigh-speed photoconductors may be used as transient current sources forradiating antennas, including dipoles, resonant dipoles, transmissionlines, tapered antennas and large-aperture photoconducting antennas.U.S. Pat. Nos. 6,144,679, 6,697,186 and 5,543,960 teach various ways inwhich second- or higher-order nonlinear optical effects in unbiasedmaterials may be employed to generate terahertz radiation.

No matter which technique is chosen, the terahertz power generated isusually on the order of microwatts, even with many watts of input power.The inability to generate significant terahertz power places mostreal-world applications out of reach. In addition, substantial coolingis required with both photoconduction and nonlinear optical frequencyconversion due to their low efficiency.

Given the above, what is needed in the art is a better technique forgenerating terahertz radiation. Further, because microwave radiationalso finds great use in a host of applications, what is needed in theart is a better technique for generating microwave radiation. Moreparticularly, what is needed in the art is a better technique forgenerating significant terahertz or microwave power.

SUMMARY OF THE INVENTION

To address the above-discussed deficiencies of the prior art, one aspectof the invention provides a negative refractive index device. In oneembodiment, the negative refractive index device includes: (1) anoptical input configured to receive light and (2) an optical mediumhaving a negative index of refraction and a second-order nonlinearityproximate (near or at) a center frequency of the light, coupled to theoptical input and configured to resonate in response to the light toyield radiation having a phase velocity based on a group velocity of thelight.

In another aspect, the invention provides a method of generatingradiation. In one embodiment, the method includes: (1) receiving lightinto an optical input and (2) receiving the light into an optical mediumhaving a negative index of refraction and a second-order nonlinearityproximate a center frequency of the light, the optical medium resonatingin response thereto to yield the radiation, the radiation having a phasevelocity based on a group velocity of the light.

In another aspect, the invention provides a negative refractive indexdevice. In one embodiment, the negative refractive index deviceincludes: (1) a light pump coupled to the optical input and configuredto generate light, (2) an optical input coupled to the light pump andconfigured to receive the light and (3) an optical medium having anegative index of refraction and a second-order nonlinearity proximate acenter frequency of the light, coupled to the optical input andconfigured to resonate in response to the light to yield radiationhaving a phase velocity based on a group velocity of the light.

The foregoing has outlined certain aspects and embodiments of theinvention so that those skilled in the pertinent art may betterunderstand the detailed description of the invention that follows.Additional aspects and embodiments will be described hereinafter thatform the subject of the claims of the invention. Those skilled in thepertinent art should appreciate that they can readily use the disclosedaspects and embodiments as a basis for designing or modifying otherstructures for carrying out the same purposes of the invention. Thoseskilled in the pertinent art should also realize that such equivalentconstructions do not depart from the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the invention, reference is nowmade to the following descriptions taken in conjunction with theaccompanying drawings, in which:

FIG. 1 illustrates a high-level block diagram of one embodiment of anegative refractive index device for generating terahertz or microwaveradiation constructed according to the principles of the invention;

FIG. 2 illustrates a pulse of light that may be provided to the negativerefractive index device of FIG. 1;

FIG. 3 illustrates a dispersion diagram of the negative refractive indexdevice of FIG. 1; and

FIG. 4 illustrates a flow diagram of one embodiment of a method ofgenerating terahertz or microwave radiation carried out according to theprinciples of the invention.

DETAILED DESCRIPTION

FIG. 1 illustrates a high-level block diagram of one embodiment of anegative refractive index device for generating terahertz or microwaveradiation constructed according to the principles of the invention.

In the illustrated embodiment, the negative refractive index devicereceives pulses of light from a light pulse source, which may be a lightpump 110. The pulses of light lie about a center frequency f_(c) andhave a certain bandwidth f_(h)-f₁. The center frequency of the pulses oflight may be between about 10¹³ Hz and about 10¹⁵ Hz. In the illustratedembodiment, the center frequency of the pulses of light is between about1.5×10¹⁴ Hz and about 6×10¹⁴ Hz. The pulses of light may have abandwidth between about 3×10⁸ Hz and about 5×10¹³ Hz. In the illustratedembodiment, the pulses of light have a bandwidth between about 5×10⁸ Hzand about 5×10¹² Hz.

In an alternative embodiment, the negative refractive index devicereceives continuous-wave light. In other embodiments, the negativerefractive index device receives combinations of pulses of light andcontinuous-wave light.

Returning to the embodiment of FIG. 1, the light pump 110 causes thepulses of light to be transmitted along an optical fiber 120 to thedevice. In an alternative embodiment, the light pump 110 may transmitthe pulses of light through free space to the device. The deviceincludes an optical coupler 130 that, in the embodiment of FIG. 1, iscoupled to the optical fiber 120. The optical coupler 130 provides atransition region for the pulses of light as they travel from theoptical fiber 120 (or free space) to a negative refractive index opticalmedium 140. In the embodiment of FIG. 1, the negative refractive indexoptical medium 140 is a metamaterial. In an alternative embodiment, thenegative refractive index optical medium 140 is a homogeneous material.The term “optical medium” as used herein therefore encompasses bothmetamaterials and homogeneous materials.

The optical medium 140 constitutes the heart of the device of FIG. 1.The optical medium 140 has a negative index of refraction (n) proximatea center frequency of the pulses of light. One way to realize a negativeindex of refraction is if the medium has both a negative electricalpermittivity (∈) and a negative magnetic permeability (μ) proximate acenter frequency of the pulses of light. The optical medium 140 alsoexhibits a second-order nonlinearity proximate the center frequency ofthe pulse of light and the output radiation of interest.

The pulses of light enter and propagate through the optical medium 140at a certain group velocity (dω/dk) that depends upon n. A resonancebegins to occur in the optical medium 140 that amounts to a special caseof three-wave mixing, a phenomenon that is known to occur in othercontexts to those skilled in the pertinent art. As a result, radiationhaving a phase velocity (ω/k) based on, or even a function of, the groupvelocity of the pulses of light is generated and begins to exit theoptical medium 140 as an arrow 150 indicates. The radiation may beterahertz radiation of between about 3×10¹¹ Hz and about 5×10¹³ Hz ormicrowave radiation of between about 3×10⁸ Hz and about 3×¹¹ Hz. In theillustrated embodiment, the radiation is terahertz radiation of betweenabout 5×10¹¹ Hz and about 5×10¹² Hz or microwave radiation of betweenabout 1×10⁹ Hz and about 1×10¹¹ Hz.

To understand the resonance that occurs within the optical medium 140,it is important to understand the structure of a representative pulse oflight and the optical properties of the optical medium. Accordingly,FIG. 2 illustrates a pulse of light 210 that may be provided to themetamaterial-based device of FIG. 1. FIG. 2 plots amplitude as afunction of frequency.

The pulse of light 210 has center frequency f_(c). On either side off_(c) lie a lower frequency f₁ and an upper frequency f_(h). Theproperties of the optical medium 140 of FIG. 1 are selected such thatlight of various frequencies between the lower and higher frequenciesf₁, f_(h) causes a resonance in the optical medium. Before discussingthose properties, it should be noted that while the pulse of light 210is illustrated as being generally Gaussian in shape, other shapes fallwithin the scope of the invention. In fact, particular embodiments ofthe invention may employ a chirped pulse of light such that the lowerand upper frequencies f₁, f_(h) are amplified with respect to theremainder of the pulse of light.

The optical medium provides the medium within which three-wave mixingoccurs with respect to the lower and upper frequencies f₁, f_(h) togenerate the output (terahertz or microwave) radiation. Therefore, theoptical medium should have certain physical properties, namely anegative n proximate the center frequency of the pulses of light and asecond-order nonlinearity; the optical medium should not rely on anadjacent structure, such as a nonlinear positive dielectric, for itssecond-order nonlinearity. The second order nonlinearity may be inherentto the optical medium, or a second-order nonlinear positive dielectricmay be embedded in the negative index medium to provide thenonlinearity.

The optical medium may thus be modeled as a Lorentz oscillator withsecond-order nonlinear susceptibility. For the inherent second-ordernonlinearity, a lossless Lorentz anharmonic oscillator model may bestcharacterize the effective nonlinear susceptibilities of the opticalmedium. That model and its nonlinear susceptibilities are described inChowdhury, et al., “Nonlinear Wave Mixing and Susceptibility Propertiesof Negative Refractive Index Materials,” Phys. Rev. E, vol. 75, 016603(2007), incorporated herein by reference.

To satisfy a long wave short wave (LWSW) resonance condition, the groupvelocity of the short wave (high frequency wave) should be equal to thephase velocity of the long wave (low frequency wave). A technique todetermine the frequencies that satisfy this condition will now be setforth.

The wave vector of a particular wave is given by:

${k(\omega)} = {\frac{\omega}{c_{0}}\sqrt{{ɛ(\omega)}{\mu (\omega)}}}$

Differentiating with respect to ω,

$\frac{k}{\omega} = {\left. {\frac{1}{c_{0}}\left\lbrack {{\omega \frac{({ɛ\mu})^{\frac{1}{2}}}{\omega}} + ({ɛ\mu})^{\frac{1}{2}}} \right\rbrack}\Rightarrow\frac{k}{\omega} \right. = {\left. {\frac{1}{c_{0}}\left\{ {{\omega \left\lbrack {\frac{1}{2}({ɛ\mu})^{- \frac{1}{2}}\left( {{ɛ\frac{\mu}{\omega}} + {\mu \frac{ɛ}{\omega}}} \right)} \right\rbrack} + ({ɛ\mu})^{\frac{1}{2}}} \right\}}\Rightarrow\frac{k}{\omega} \right. = {\left. {\frac{1}{c_{0}}\left\lbrack {{\frac{\omega}{2({ɛ\mu})^{\frac{1}{2}}}\left( {{ɛ\frac{\mu}{\omega}} + {\mu \frac{ɛ}{\omega}}} \right)} + ({ɛ\mu})^{\frac{1}{2}}} \right\rbrack}\Rightarrow\frac{k}{\omega} \right. = {\left\{ {{\frac{\omega}{2c_{0}}\left\lbrack {{\left( \frac{ɛ}{\mu} \right)^{\frac{1}{2}}\frac{\mu}{\omega}} + {\left( \frac{\mu}{ɛ} \right)^{\frac{1}{2}}\frac{ɛ}{\omega}}} \right\rbrack} + \frac{({ɛ\mu})^{\frac{1}{2}}}{c_{0}}} \right\}.}}}}$

For LWSW resonance,

${\frac{\omega_{s}}{k} = \frac{\omega_{l}}{k_{l}}},$

where the subscript “s” refers to the short wave (which lies on thenegative branch in the negative index media case, illustrated in FIG. 3)and the subscript “1” refers to the long wave (which lies on the lowerpositive branch in the negative index media case, also illustrated inFIG. 3). It should be noted that the term

$({ɛ\mu})^{\frac{1}{2}}$

is equal to

$- \left( {({ɛ\mu})^{\frac{1}{2}}} \right)$

when the frequency at which ∈ and μ are evaluated has a negative indexof refraction.

$\left. \Rightarrow\frac{k_{s}}{\omega} \right. = {\left. \frac{k_{l}}{\omega_{l}}\Rightarrow{{\frac{\omega_{s}}{2c_{0}}\left\lbrack {{\left( \frac{ɛ_{s}}{\mu_{s}} \right)^{\frac{1}{2}}\frac{\mu_{s}}{\omega}} + {\left( \frac{\mu_{s}}{ɛ_{s}} \right)^{\frac{1}{2}}\frac{ɛ_{s}}{\omega}}} \right\rbrack} - \frac{\left( {\left( {ɛ_{s}\mu_{s}} \right)^{\frac{1}{2}}} \right)}{c_{0}}} \right. = \frac{k_{l}}{\omega_{l}}}$${{But}\mspace{14mu} \frac{k_{l}}{\omega_{l}}} = {\left. \frac{\left( {ɛ_{l}\mu_{l}} \right)^{\frac{1}{2}}}{c_{0}}\Rightarrow{{\frac{\omega_{s}}{2c_{0}}\left\lbrack {{\left( \frac{ɛ_{s}}{\mu_{s}} \right)^{\frac{1}{2}}\frac{\mu_{s}}{\omega}} + {\left( \frac{\mu_{s}}{ɛ_{s}} \right)^{\frac{1}{2}}\frac{ɛ_{s}}{\omega}}} \right\rbrack} - \frac{\left( {\left( {ɛ_{s}\mu_{s}} \right)^{\frac{1}{2}}} \right)}{c_{0}}} \right. = {\left. \frac{\left( {ɛ_{l}\mu_{l}} \right)^{\frac{1}{2}}}{c_{0}}\Rightarrow{{\frac{\omega_{s}}{2}\left\lbrack {{\left( \frac{ɛ_{s}}{\mu_{s}} \right)^{\frac{1}{2}}\frac{\mu_{s}}{\omega}} + {\left( \frac{\mu_{s}}{ɛ_{s}} \right)^{\frac{1}{2}}\frac{ɛ_{s}}{\omega}}} \right\rbrack} - \left( {\left( {ɛ_{s}\mu_{s}} \right)^{\frac{1}{2}}} \right)} \right. = {\left( {ɛ_{l}\mu_{l}} \right)^{\frac{1}{2}}.}}}$

The above expression is the LWSW resonance condition in terms of thepermittivity ∈ and permeability μ of the medium.

To exemplify the technique for determining the frequencies that satisfythe LWSW resonance condition further, it will be assumed that for anactual or effective medium, permittivity ∈ may be expressed as

${{ɛ(\omega)} = {ɛ_{0}\frac{\omega^{2} - \omega_{a}^{2}}{\omega^{2} - \omega_{0}^{2}}}},$

and permeability μ may be expressed as

${\mu (\omega)} = {\mu_{0}{\frac{\omega^{2} - \omega_{b}^{2}}{\omega^{2} - \Omega^{2}}.}}$

Differentiating the permittivity with respect to ω,

$\frac{ɛ}{\omega} = {\left. {{ɛ_{0}\left\lbrack {{\left( {\omega^{2} - \omega_{a}^{2}} \right)\left( {- 1} \right)\left( {\omega^{2} - \omega_{0}^{2}} \right)^{- 2}\left( {2\omega} \right)} + {\left( {\omega^{2} - \omega_{0}^{2}} \right)^{- 1}\left( {2\omega} \right)}} \right\rbrack}.}\Rightarrow\frac{ɛ}{\omega} \right. = {\left. {ɛ_{0}\left\lbrack {\frac{{- 2}{\omega \left( {\omega^{2} - \omega_{a}^{2}} \right)}}{\left( {\omega^{2} - \omega_{0}^{2}} \right)^{2}} + \frac{2\omega}{\left( {\omega^{2} - \omega_{0}^{2}} \right)}} \right\rbrack}\Rightarrow\frac{ɛ}{\omega} \right. = {\left. {2ɛ_{0}{\omega \left\lbrack {\frac{1}{\left( {\omega^{2} - \omega_{0}^{2}} \right)} - \frac{\left( {\omega^{2} - \omega_{a}^{2}} \right)}{\left( {\omega^{2} - \omega_{0}^{2}} \right)^{2}}} \right\rbrack}}\Rightarrow\frac{ɛ}{\omega} \right. = {2ɛ_{0}\omega {\frac{\left( {\omega_{a}^{2} - \omega_{0}^{2}} \right)}{\left( {\omega^{2} - \omega_{0}^{2}} \right)^{2}}.}}}}}$

Similarly, the derivative of the permeability is given by:

$\frac{\mu}{\omega} = {2\mu_{0}\omega {\frac{\left( {\omega_{b}^{2} - \Omega^{2}} \right)}{\left( {\omega^{2} - \Omega^{2}} \right)^{2}}.}}$

The LWSW resonance condition can now be written as:

${{\left\lbrack {ɛ_{0}\mu_{0}\frac{\left( {\omega_{s}^{2} - \omega_{a}^{2}} \right)\left( {\omega_{s}^{2} - \Omega^{2}} \right)}{\left( {\omega_{s}^{2} - \omega_{0}^{2}} \right)\left( {\omega_{s}^{2} - \omega_{b}^{2}} \right)}} \right\rbrack^{\frac{1}{2}}\omega_{s}^{2}\frac{\left( {\omega_{b}^{2} - \Omega^{2}} \right)}{\left( {\omega_{s}^{2} - \Omega^{2}} \right)^{2}}} + {\left\lbrack {ɛ_{0}\mu_{0}\frac{\left( {\omega_{s}^{2} - \omega_{0}^{2}} \right)\left( {\omega_{s}^{2} - \omega_{b}^{2}} \right)}{\left( {\omega_{s}^{2} - \omega_{a}^{2}} \right)\left( {\omega_{s}^{2} - \Omega^{2}} \right)}} \right\rbrack^{\frac{1}{2}}\omega_{s}^{2}\frac{\left( {\omega_{a}^{2} - \omega_{0}^{2}} \right)}{\left( {\omega_{s}^{2} - \omega_{0}^{2}} \right)^{2}}}} = {\left\lbrack {ɛ_{0}\mu_{0}\frac{\left( {\omega_{l}^{2} - \omega_{a}^{2}} \right)\left( {\omega_{l}^{2} - \omega_{b}^{2}} \right)}{\left( {\omega_{l}^{2} - \omega_{0}^{2}} \right)\left( {\omega_{l}^{2} - \Omega^{2}} \right)}} \right\rbrack^{\frac{1}{2}} + {\left\lbrack {ɛ_{0}\mu_{0}\frac{\left( {\omega_{s}^{2} - \omega_{a}^{2}} \right)\left( {\omega_{s}^{2} - \omega_{b}^{2}} \right)}{\left( {\omega_{s}^{2} - \omega_{0}^{2}} \right)\left( {\omega_{s}^{2} - \Omega^{2}} \right)}} \right\rbrack^{\frac{1}{2}}}}$

Given the parameters ω_(o), ω_(a), ω_(b) and Ω, the pair(s) offrequencies (ω_(s), ω₁) that satisfy the above condition can be foundnumerically.

Those skilled in the art, given the above disclosure, will understandthat a variety of optical medium structures can provide the physicalproperties described above. The invention is not limited to a particularstructure and, indeed, encompasses various metamaterials and otheroptical media.

FIG. 3 illustrates a dispersion diagram of the optical medium 140 in thedevice of FIG. 1. Assuming the optical medium exhibits a permittivity ∈given by:

${ɛ(\omega)} = {ɛ_{0}\frac{\omega^{2} - \omega_{a}^{2}}{\omega^{2} - \omega_{0}^{2}}}$

and a permeability p given by:

${{\mu (\omega)} = {\mu_{0}\frac{\omega^{2} - \omega_{b}^{2}}{\omega^{2} - \Omega^{2}}}},$

where ω_(a) and ω_(b) are cutoff frequencies and ω_(o) and Ω areresonant frequencies, the dispersion relation is given by:

${k(\omega)} = {{\pm \frac{\omega}{c}}{\sqrt{\frac{\left( {\omega^{2} - \omega_{a}^{2}} \right)}{\left( {\omega^{2} - \omega_{a}^{2}} \right)}\frac{\left( {\omega^{2} - \omega_{b}^{2}} \right)}{\left( {\omega^{2} - \Omega^{2}} \right)}}.}}$

Two curves 310, 320 illustrate this dispersion relation. The curve 310pertains to the pulses of light and has a negative branch so labeled. Agroup velocity (dω/dk) vector 330 lies along the curve 310 and appliesto the pulses of light. The curve 320 pertains to the radiation and hasa lower branch so labeled. A phase velocity (ω/k) vector 340 bridges twopoints on the curve 320 and applies to the radiation that results fromthe three-wave mixing. The group velocity (dω/dk) vector 330 and thephase velocity (ω/k) vector 340 are parallel one another, which is acondition necessary for setting up the long wave short wave resonancethat occurs in the optical medium.

FIG. 4 illustrates a flow diagram of one embodiment of a method ofgenerating terahertz or microwave radiation carried out according to theprinciples of the invention. The method begins in a start step 410. In astep 420, a pulse of light is generated, perhaps with a light pumpcoupled to the optical input. In a step 430, the pulse of light istransmitted to an optical input, perhaps via an optical fiber. In a step440, the pulse of light is received into the optical input. In a step450, the pulse of light is received into an optical medium. As statedabove, the optical medium has a negative index of refraction and asecond-order nonlinearity proximate a center frequency of the pulse oflight. In a step 460, the optical medium resonates in response theretoto yield radiation having a phase velocity based on a group velocity ofthe pulse of light. As the step 460 indicates, the radiation may beterahertz or microwave radiation. The method ends in an end step 470.

Those skilled in the art to which the invention relates will appreciatethat other and further additions, deletions, substitutions andmodifications may be made to the described embodiments without departingfrom the scope of the invention.

1. A negative refractive index device, comprising: an optical inputconfigured to receive light; and an optical medium having a negativeindex of refraction and a second-order nonlinearity proximate a centerfrequency of said light, coupled to said optical input and configured toresonate in response to said light to yield radiation having a phasevelocity based on a group velocity of said light.
 2. The device asrecited in claim 1 further comprising an optical fiber coupled to saidoptical input.
 3. The device as recited in claim 1 wherein said centerfrequency is between about 10¹³ Hz and about 10¹⁵ Hz.
 4. The device asrecited in claim 1 wherein said light has a bandwidth between about3×10⁸ Hz and about 5×10¹³ Hz.
 5. The device as recited in claim 1wherein said radiation is selected from the group consisting of:terahertz radiation of between about 0.3 to about 50 terahertz, andmicrowave radiation of between about 3×108 Hz and about 3×10¹¹ Hz. 6.The device as recited in claim 1 further comprising a light pump coupledto said optical input and configured to generate pulses of said light.7. A method of generating radiation, comprising: receiving light into anoptical input; and receiving said light into an optical medium having anegative index of refraction and a second-order nonlinearity proximate acenter frequency of said light, said optical medium resonating inresponse thereto to yield said radiation, said radiation having a phasevelocity based on a group velocity of said light.
 8. The method asrecited in claim 7 further comprising transmitting said light to saidoptical input via an optical fiber.
 9. The method as recited in claim 7wherein said center frequency is between about 10¹³ Hz and about 10¹⁵Hz.
 10. The method as recited in claim 7 wherein said light has abandwidth between about 3×10⁸ Hz and about 5×10¹³ Hz.
 11. The method asrecited in claim 7 wherein said radiation is selected from the groupconsisting of: terahertz radiation of between about 0.3 to about 50terahertz, and microwave radiation of between about 3×10⁸ Hz and about3×10¹¹Hz.
 12. The method as recited in claim 7 further comprisinggenerating said light with a light pump coupled to said optical inputand configured to generate pulses of said light.
 13. A negativerefractive index device, comprising: a light pump coupled to saidoptical input and configured to generate pulses of light; an opticalinput coupled to said light pump and configured to receive said pulsesof light; and an metamaterial having a negative index of refraction anda second-order nonlinearity proximate a center frequency of said light,coupled to said optical input and configured to resonate in response tosaid pulses of light to yield radiation having a phase velocity based ona group velocity of said pulses of light.
 14. The device as recited inclaim 13 further comprising an optical fiber coupled between said lightpump and said optical input.
 15. The device as recited in claim 13wherein said center frequency is between about 10¹³ Hz and about 10¹⁵Hz.
 16. The device as recited in claim 15 wherein said center frequencyis between about 1.5×10¹⁴ Hz and about 6×10¹⁴ Hz.
 17. The device asrecited in claim 13 wherein said light has a bandwidth between about3×10⁸ Hz and about 5×10¹³ Hz.
 18. The device as recited in claim 17wherein said light has a bandwidth between about 5×10⁸ Hz and about5×10¹² Hz.
 19. The device as recited in claim 13 wherein said radiationis selected from the group consisting of: terahertz radiation of betweenabout 0.3 to about 50 terahertz, and microwave radiation of betweenabout 3×10⁸ Hz and about 3×10¹¹ Hz.
 20. The device as recited in claim19 wherein said radiation is selected from the group consisting of:terahertz radiation of between about 5×10¹¹ Hz and about 5×10¹² Hz, andmicrowave radiation of between about 1×10⁹ Hz and about 1×10¹¹ Hz.